Examples, where interpolation of complex numbers or symbols is performed are numerous. For example, in wireless mobile telecommunication systems, the data samples or data symbols may be provided at a relative low rate (e.g. 30.72 MHz for LTE20) within the baseband, while the frequency of the carrier is significantly higher (for example 1 . . . 2 GHz). When the data represented by complex numbers or complex-valued symbols is to be processed so as to be transmitted by means of the carrier with a high frequency, interpolation between the complex-valued samples or symbols of the baseband signal may be used to generate a trajectory connecting the interpolated complex-valued samples in the constellation diagram. The trajectory may be modulated on the carrier frequency so as to wirelessly transmit the complex-valued samples at the carrier frequency.
In mobile telecommunication applications, an in-phase (I) and a quadrature (Q) component of the complex-valued samples are often processed individually before being modulated on the carrier. To this end, also interpolation between subsequent I- and Q-components of the complex values may be performed separately, e.g. the I-components of the interpolated complex-valued samples may be determined using only the I-components of the neighboring samples.
Other implementations use a R,φ-representation of the complex-valued samples in order to directly generate the transmit signal at the carrier frequency digitally. That is, a complex-valued sample is represented by a radius value R giving its distance from the origin within the constellation diagram and by an angle φ with respect to a predetermined axis of the complex plane. For an R/φ-representation, the concept to interpolate radius components of complex values using only R-components of the neighboring complex samples (φ likewise) may introduce systematic errors and. Even if the interpolation accuracy and the number of interpolated samples between two neighboring complex-valued samples is increased, the spectrum of the resultant interpolated signal may exhibit a significant error contribution which may violate a spectral requirement for the transmit spectrum of the so-generated signal. There may be a desire to improve the determination of interpolated complex-valued samples.